shock wave, that is, a shock wave whose strength is reduced by an overtaking
rarefaction or expansion wave. Friedrichs’ treatment of this problem, which will be
briefly discussed below, gives quite accurate results if the shock is weak or of
moderate strength. Friedrichs’ method is based on the fact that the flow properties
behind a weak shock and the flow properties behind a simple wave agree up to
terms of second order in the shock strength (see Sect. 3.12, Chap. 3). The progress
of a decaying shock wave can be represented by shocks of varying strength and any
individual shock wave can be identified according to its shock speed. In Friedrichs’
method these individual shock waves are replaced by simple waves that have the
same flow properties behind it as the shocks themselves. The flow of these simple
Fig. 4.52 Variation of
particle velocity within the
shock wave zone (see text)
Fig. 4.53 Plots of particle velocity as a function of position at three different times with u p ¼ 0.3
(see text)
194
4 Numerical Treatment of Plane Shocks
rarefaction or expansion wave. Friedrichs’ treatment of this problem, which will be
briefly discussed below, gives quite accurate results if the shock is weak or of
moderate strength. Friedrichs’ method is based on the fact that the flow properties
behind a weak shock and the flow properties behind a simple wave agree up to
terms of second order in the shock strength (see Sect. 3.12, Chap. 3). The progress
of a decaying shock wave can be represented by shocks of varying strength and any
individual shock wave can be identified according to its shock speed. In Friedrichs’
method these individual shock waves are replaced by simple waves that have the
same flow properties behind it as the shocks themselves. The flow of these simple
Fig. 4.52 Variation of
particle velocity within the
shock wave zone (see text)
Fig. 4.53 Plots of particle velocity as a function of position at three different times with u p ¼ 0.3
(see text)
194
4 Numerical Treatment of Plane Shocks